-3r^2-r+14=0

Solution for -3r^2-r+14=0 equation:

-3r^2-r+14=0

We add all the numbers together, and all the variables

-3r^2-1r+14=0

a = -3; b = -1; c = +14;
Δ = b2-4ac
Δ = -12-4·(-3)·14
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*-3}=\frac{-12}{-6}
=+2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*-3}=\frac{14}{-6}
=-2+1/3
$